I think the next step is to check the buckling of the shear web.
So far we have calculated the following stresses in the web:
Shear Stress = 2725 psi (limit) and 4088 psi (ultimate)
Bending Stress at top and bottom edge of the web = 16094 psi (Limit) and 24141 psi (ultimate)
To begin I will reproduce the figure from yesterdays post that provides all the dimensions of the web at the wing root.
The web is 10.5" deep and 0.025" thick.
Initially ignore the stiffeners and assume that the web is unstiffened between the ribs as an example to show the effect of stiffening. So the length is initially 21 in long.
Calculate Buckling Stress Due to Web Shear (No Stiffeners):
The calculations are done in a spreadsheet but this formatted similarly to a hand written calculation and it is easily followed.
The edges of the web secured by rivets have been assumed to have edge fixity mid way between a hinged and clamped edge.
Note that the shear stress in the web (2725 psi limit and 4088 psi) is substantially higher than the buckling stress 460.5 psi. This buckling stress does not mean that the web fails at this stress but it buckles out of plane and there is a loss of stiffness and its ability to carry higher loads is reduced. A tension field would form in the web if loading progressed to higher loads (i.e. the web would start to develop wrinkles at 45 deg).
Note also that the wave length of the buckles is 13.125".
Calculate Buckling Stress Due to Web Bending:
Clearly the buckling stress (2357.4 psi) is much lower than the applied bending stress of 16094 psi (limit) and 24141 psi (ultimate).
The wave length of the buckling is 7 inches.
Use of Stiffeners:
Given the wave length of the shear and bending buckling, 13.125" and 7" respectively, closely spaced stiffeners can be added to help control the buckling and hold the web in a planar position to increase the buckling stresses. In this case vertical stiffeners have been added in the root area at 2" spacing. The stiffeners are 0.5" x 0.5" x 0.025" angles.
Repeat Shear Buckling Calculations For Small Panels:
With stiffeners installed, the shear web is now divided into smaller panels 2" wide and 10.5" high.
The shear buckling calculations are repeated for these smaller panels.
Note that the critical buckling stress in shear is now 11332 psi which is substantially higher than the applied applied shear stresses of (2725 psi limit and 4088 psi). So the stiffeners have prevented shear buckling.
Repeat Bending Buckling Calculations For Small Panels:
There is no improvement in the buckling stress due to the addition of the stiffeners. So the additional of the stiffeners will not prevent the web from buckling due to the bending stresses. The stiffeners will control the magnitude of the buckles and enforce a shorter wavelength but do not eliminate the web buckling. Again this does not mean that the spar web will fail - it can continue to sustain higher loads once the initial buckling stress has been passed but additional bending load added after buckling will need to be carried by the caps.
If longitudinal stiffeners are added to further divide the web into smaller panels, higher stresses can be achieved prior to the web buckling.
Consider adding 2 x longitudinal stiffeners equally spaced between the caps to divide the 10.5" web dimension into 3 spaces (i.e. 10.5/3 = 3.5). The resulting shear panels are now 2" x 3.5".
The buckling stress has now increased to 21215 psi. So the web would now remain unbuckled to a point approx midway between limit load (16094 psi) and the ultimate load (24141 psi). A decision will need to be made on whether to add these stiffeners or just let the web buckle. This decision might be influenced by further load testing during which the web buckling can be monitored. Remember that it has been verified by previous calculations that the edges of of the shear web is adequately secured by the rivets to prevent inter rivet buckling. So the web buckling due to bending will be characterized by buckles inboard of the caps between the stiffeners.
Web Stiffener Sizing:
Check the size of the web stiffeners to ensure that they have sufficient stiffness to control web buckling:
The size of the web stiffeners is more than adequate.
Rivet spacing does not comply with the suggested spacing. Again the effects of this can be monitored in future load testing.